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Block #784,039

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/26/2014, 3:00:18 PM Β· Difficulty 10.9751 Β· 6,029,919 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
dce08ed8da540a1e2a3992234e1fee66dee3600ef4b6958ec45591ae45049159
View on Chainz β†—

Height

#784,039

Difficulty

10.975052

Transactions

2

Size

581 B

Version

2

Bits

0af99cfc

Nonce

1,210,441,698

Timestamp

10/26/2014, 3:00:18 PM

Confirmations

6,029,919

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c66f6679484bba4141c14cd3beadcf465ddc81b85afaebf989937c545bbc6a29
Transactions (2)
Coinbased55432bf6631b1…3445b348154fb3
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
cac2b4cd6cc2e8…776d1172b3b75c
2 in β†’ 2 out19.8700 XPM373 B
AcAFW717…V1pWEX3JAct4faog…9GdAzg1c
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.227 Γ— 10⁹⁹(100-digit number)
32277378725831948891…85984212050422333439
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.227 Γ— 10⁹⁹(100-digit number)
32277378725831948891…85984212050422333439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.227 Γ— 10⁹⁹(100-digit number)
32277378725831948891…85984212050422333441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
6.455 Γ— 10⁹⁹(100-digit number)
64554757451663897783…71968424100844666879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.455 Γ— 10⁹⁹(100-digit number)
64554757451663897783…71968424100844666881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.291 Γ— 10¹⁰⁰(101-digit number)
12910951490332779556…43936848201689333759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.291 Γ— 10¹⁰⁰(101-digit number)
12910951490332779556…43936848201689333761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.582 Γ— 10¹⁰⁰(101-digit number)
25821902980665559113…87873696403378667519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.582 Γ— 10¹⁰⁰(101-digit number)
25821902980665559113…87873696403378667521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.164 Γ— 10¹⁰⁰(101-digit number)
51643805961331118226…75747392806757335039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.164 Γ— 10¹⁰⁰(101-digit number)
51643805961331118226…75747392806757335041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.032 Γ— 10¹⁰¹(102-digit number)
10328761192266223645…51494785613514670079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,755,741 XPMΒ·at block #6,813,957 Β· updates every 60s
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